The Composition Operators on the Space of Dirichlet Series with Square Summable Coefficients

摘要

In this paper, a complete answer to this question is found. In the process, we encounter the space D of functions f, which in some (possibly remote) halfplane Cθ = { s ∈ C : Ks > θ }(θ ∈ R } admit representation by a convergent Dirich- let series (0.l). It is, in a sense, a space of germs of holomorphic functions. It is important to note that if a Dirichlet series converges on Cθ then it converges ab- solutely and uniformly on Cθ, provided v > θ + 1 (see e.g. [3]).